∫ - E) ^ (- 3x / 2) DX how to calculate?

∫ - E) ^ (- 3x / 2) DX how to calculate?

What is the derivative of F (x) = a ^ x? F (x) = a ^ x is an exponential function, a > 0 and a ≠ 1

∫ [3x ^ 2 / (1 + x ^ 2) DX why is 3x-3arctanx + C?
∫[3x^2/(1+x^2)dx=∫[3-3/(1+x^2)]dx=3∫[1-1/(1+x^2)]dx=3[(x+c)-(arctanx+c)]=3x-3arctanx
Why is there a C after the correct answer

Because inverse integral can have many answers
For example, (X & # 178; + 5) '= 2x + 0 = 2x
(x²-0.124)'=2x.
The results of the two formulas are the same, when the inverse operation, we need to add C. to express rigor

How to prove that two straight lines are perpendicular in space rectangular coordinate system

If a (x1, Y1, z1), B (X2, Y2, Z2) AB, a direction vector is (x2-x1, y2-y1, z2-z1) if C (X3, Y3, Z3), D (x4, Y4, Z4) CD, a direction vector is (x4-x3, y4-y3, z4-z3), we only need to prove AB * CD = (x2-x1) (x4-x3) + (...)

How to represent a straight line in space rectangular coordinate system?

The plane equation in space rectangular coordinate system is ax + by + CZ + D = 0
The general equation of spatial straight line is as follows
Two plane equations, representing a straight line (intersection)
The plane equation in space rectangular coordinate system is ax + by + CZ + D = 0
The linear equation is: a1x + b1y + c1z + D1 = 0, a2x + b2y + c2z + D2 = 0, simultaneous
(simultaneous results can be expressed as determinants)
The standard formula of spatial straight line: (similar to the oblique formula of point in plane coordinate system)
(x-x0)/a＝(y-y0)/b＝(z-z0)/c
Where (a, B, c) are direction vectors
Two point formula of spatial straight line: (similar to two point formula in plane coordinate system)
(x-x1)/(x-x2)＝(y-y1)/(y-y2)＝(z-z1)/(z-z2)

In the space rectangular coordinate system, given the coordinates of two points, how to get the midpoint coordinates and prove it?
You need proof,
Space rectangular coordinate system! It's space. To prove

[(x1+x2)/2,(y1+y2)/2,(z1+z2)/2]
Two points in space can be analyzed in the same plane, which can be proved by plane rectangular coordinate system

In the space rectangular coordinate system, how to prove that two straight lines are parallel, with what judgment?

L1 (x1, Y1, z1) L2 (X2, Y2, Z2) has X1 / x2 = Y1 / y2 = Z1 / Z2

A problem of vector rotation in three dimensional coordinate system
In a three-dimensional space coordinate system, there is a space vector starting from the origin, and the coordinates are known. It is necessary to rotate the coordinate system a degree around the Y axis, and then B degree around the Z axis of the rotated coordinate system, so that the X direction of the final coordinate system coincides with the initial space vector, and the angles a and B of two rotations are calculated

It depends on the coordinates of this vector. In general, we first rotate the xoy plane to coincide with the known vector, and then rotate the YOZ plane to coincide with the known vector. As for a and B, we can calculate them from the initial coordinates of the known vector

In three-dimensional space, at zero crossing point, how to express the straight line that is 45 degrees to the positive direction of x-axis and y-axis

X = y, z = 0 and x = - y, z = 0

Formula of distance between two points in three dimensional coordinates

Let a (x1, Y1, z1), B (X2, Y2, Z2), then the distance between a and B is
d=√[(x1-x2)^2+(y1-y2)^2+(z1-z2)^2]

In the space rectangular coordinate system, the trajectory equation of the moving point whose distance to the y-axis is four times that to the z-axis?

Let the coordinates of the moving point be (x, y, z)
Then we get √ (X & # 178; + Z & # 178;) = 4 √ (X & # 178; + Y & # 178;)
The result is 15x & # 178; + 16y & # 178; - Z & # 178; = 0